Solve for $x$ and $y$ using elimination. ${-2x-5y = -52}$ ${2x+3y = 36}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $-2y = -16$ $\dfrac{-2y}{{-2}} = \dfrac{-16}{{-2}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-2x-5y = -52}\thinspace$ to find $x$ ${-2x - 5}{(8)}{= -52}$ $-2x-40 = -52$ $-2x-40{+40} = -52{+40}$ $-2x = -12$ $\dfrac{-2x}{{-2}} = \dfrac{-12}{{-2}}$ ${x = 6}$ You can also plug ${y = 8}$ into $\thinspace {2x+3y = 36}\thinspace$ and get the same answer for $x$ : ${2x + 3}{(8)}{= 36}$ ${x = 6}$